Submission #75458735

Source Code Expand

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import sys
def main():
    input_data = sys.stdin.read().split()
    if not input_data:
        return
    
    N = int(input_data[0])
    S = input_data[1]
    MOD = 998244353
    MAX = N + 5
    fact = [1] * MAX
    inv = [1] * MAX
    pow2 = [1] * MAX
    for i in range(1, MAX):
        fact[i] = (fact[i - 1] * i) % MOD
        pow2[i] = (pow2[i - 1] * 2) % MOD
    inv[MAX - 1] = pow(fact[MAX - 1], MOD - 2, MOD)
    for i in range(MAX - 2, -1, -1):
        inv[i] = (inv[i + 1] * (i + 1)) % MOD
    L_counts = {}
    total_dot = 0
    for part in S.split('x'):
        l = len(part)
        if l > 0:
            L_counts[l] = L_counts.get(l, 0) + 1
            total_dot += l
    max_L = max(L_counts.keys()) if L_counts else 0
    ans_list = []
    f_prev = 1 
    
    for k in range(1, N + 1):
        if k >= max_L:
            f_curr = pow2[total_dot]
 
 
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import sys

def main():
    input_data = sys.stdin.read().split()
    if not input_data:
        return
    
    N = int(input_data[0])
    S = input_data[1]

    MOD = 998244353

    MAX = N + 5
    fact = [1] * MAX
    inv = [1] * MAX
    pow2 = [1] * MAX

    for i in range(1, MAX):
        fact[i] = (fact[i - 1] * i) % MOD
        pow2[i] = (pow2[i - 1] * 2) % MOD

    inv[MAX - 1] = pow(fact[MAX - 1], MOD - 2, MOD)
    for i in range(MAX - 2, -1, -1):
        inv[i] = (inv[i + 1] * (i + 1)) % MOD

    L_counts = {}
    total_dot = 0
    for part in S.split('x'):
        l = len(part)
        if l > 0:
            L_counts[l] = L_counts.get(l, 0) + 1
            total_dot += l

    max_L = max(L_counts.keys()) if L_counts else 0

    ans_list = []
    f_prev = 1 
    
    for k in range(1, N + 1):
        if k >= max_L:
            f_curr = pow2[total_dot]
        else:
            f_curr = 1
            for L, c in L_counts.items():
                if L <= k:
                    ways = pow2[L]
                else:
                    res1 = 0
                    limit1 = L // (k + 2)
                    for i in range(limit1 + 1):
                        term = fact[L - i * (k + 1)] * inv[i] % MOD * inv[L - i * (k + 2)] % MOD * pow2[L - i * (k + 2)] % MOD
                        if i & 1:
                            res1 = (res1 - term) % MOD
                        else:
                            res1 = (res1 + term) % MOD
                    
                    L2 = L - k - 1
                    res2 = 0
                    if L2 >= 0:
                        limit2 = L2 // (k + 2)
                        for i in range(limit2 + 1):
                            term = fact[L2 - i * (k + 1)] * inv[i] % MOD * inv[L2 - i * (k + 2)] % MOD * pow2[L2 - i * (k + 2)] % MOD
                            if i & 1:
                                res2 = (res2 - term) % MOD
                            else:
                                res2 = (res2 + term) % MOD
                    
                    ways = (res1 - res2) % MOD
                
                if c == 1:
                    f_curr = (f_curr * ways) % MOD
                else:
                    f_curr = (f_curr * pow(ways, c, MOD)) % MOD

        ans = (f_curr - f_prev) % MOD
        ans_list.append(str((ans + MOD) % MOD))
        f_prev = f_curr

    sys.stdout.write('\n'.join(ans_list) + '\n')

if __name__ == '__main__':
    main()

Submission Info

Judge Result